grouping texture nodes changes the coordinate space
Based on Gandalf3's comment I have to change the socket to blue to work around this bug.  Unfortunately, based on Setting Group Node Socket Type I conclude there is no procedure to change the type of an existing socket in 2.74.

We must add a node to the group that has a blue (vector) input.  The texture Output node is suited to the task.  Connect that input to the blank input on the Group Input and a vector input is created to match it.  Wire the blue input into the various places that the yellow goes, and then delete the yellow input from the node group.  You can delete the Output node now.  Shift-tab out to the rest of the nodes and connect the coordinates to the now-blue input of the group.

When constructing groups in the future, a solution is to shift-drag across the connection between the vector output and the Separate RGBA node's input. This creates a blue Reroute node. Including the reroute node during the creation of the group codes the input as blue (vector).